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Knapsack polytopes: a survey

Author

Listed:
  • Christopher Hojny

    (Technische Universität Darmstadt)

  • Tristan Gally

    (Technische Universität Darmstadt)

  • Oliver Habeck

    (Technische Universität Darmstadt)

  • Hendrik Lüthen

    (Technische Universität Darmstadt)

  • Frederic Matter

    (Technische Universität Darmstadt)

  • Marc E. Pfetsch

    (Technische Universität Darmstadt)

  • Andreas Schmitt

    (Technische Universität Darmstadt)

Abstract

The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy a given single linear inequality with non-negative coefficients. This paper provides a comprehensive overview of knapsack polytopes. We discuss basic polyhedral properties, (lifted) cover and other valid inequalities, cases for which complete linear descriptions are known, geometric properties for small dimensions, and connections to independence systems. We also discuss the generalization to (mixed-)integer knapsack polytopes and variants.

Suggested Citation

  • Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-019-03380-2
    DOI: 10.1007/s10479-019-03380-2
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    Cited by:

    1. Wei-Kun Chen & Liang Chen & Yu-Hong Dai, 2023. "Lifting for the integer knapsack cover polyhedron," Journal of Global Optimization, Springer, vol. 86(1), pages 205-249, May.

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